$\dfrac{ 8l + 6m }{ 9 } = \dfrac{ 5l + 10n }{ -2 }$ Solve for $l$.
Multiply both sides by the left denominator. $\dfrac{ 8l + 6m }{ {9} } = \dfrac{ 5l + 10n }{ -2 }$ ${9} \cdot \dfrac{ 8l + 6m }{ {9} } = {9} \cdot \dfrac{ 5l + 10n }{ -2 }$ $8l + 6m = {9} \cdot \dfrac { 5l + 10n }{ -2 }$ Multiply both sides by the right denominator. $8l + 6m = 9 \cdot \dfrac{ 5l + 10n }{ -{2} }$ $-{2} \cdot \left( 8l + 6m \right) = -{2} \cdot 9 \cdot \dfrac{ 5l + 10n }{ -{2} }$ $-{2} \cdot \left( 8l + 6m \right) = 9 \cdot \left( 5l + 10n \right)$ Distribute both sides $-{2} \cdot \left( 8l + 6m \right) = {9} \cdot \left( 5l + 10n \right)$ $-{16}l - {12}m = {45}l + {90}n$ Combine $l$ terms on the left. $-{16l} - 12m = {45l} + 90n$ $-{61l} - 12m = 90n$ Move the $m$ term to the right. $-61l - {12m} = 90n$ $-61l = 90n + {12m}$ Isolate $l$ by dividing both sides by its coefficient. $-{61}l = 90n + 12m$ $l = \dfrac{ 90n + 12m }{ -{61} }$ Swap signs so the denominator isn't negative. $l = \dfrac{ -{90}n - {12}m }{ {61} }$